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**Basis risk in static versus dynamic longevity-risk hedging.**
*(English)*
Zbl 1401.91129

Summary: This paper provides a tractable, parsimonious model for assessing basis risk in longevity and its effect on the hedging strategies of pension funds and annuity providers. Basis risk is captured by a single parameter, that measures the co-movement between the portfolio and the reference population’s longevity. The paper sets out the static, full and customized swap-hedge for an annuity, and compares it with a dynamic, partial, and index-based hedge. We calibrate our model to the UK and Scottish populations. The effectiveness of static versus dynamic strategies depends on the rebalancing frequency of the second, on the relative costs, and on basis risk, which does not affect fully-customized, static hedges. We show that appropriately calibrated dynamic hedging strategies can still be reasonably effective, even at low rebalancing frequencies.

### MSC:

91B30 | Risk theory, insurance (MSC2010) |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

91D20 | Mathematical geography and demography |

91G20 | Derivative securities (option pricing, hedging, etc.) |

### Keywords:

longevity risk; customized vs. indexed hedge; longevity swaps; longevity bonds; rebalancing frequency
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\textit{C. De Rosa} et al., Scand. Actuar. J. 2017, No. 4, 343--365 (2017; Zbl 1401.91129)

### References:

[1] | Barrieu, P., Bensusan, H., El Karoui, N., Hillairet, C., Loisel, S., Ravanelli, C. & Salhi, Y. (2012). Understanding, modelling and managing longevity risk: key issues and main challenges. Scandinavian Actuarial Journal3, 203-231. · Zbl 1277.91073 |

[2] | Blake, D. & Burrows, W. (2001). Survivor bonds: helping to hedge mortality risk. Journal of Risk and Insurance68, 339-348. |

[3] | Cairns, A. J., Dowd, K., Blake, D. & Coughlan, G. D. (2014). Longevity hedge effectiveness: a decomposition. Quantitative Finance14(2), 217-235. · Zbl 1294.91072 |

[4] | Coughlan, G. D., Khalaf-Allah, M., Ye, Y., Kumar, S., Cairns, A. J., Blake, D. & Dowd, K. (2011). Longevity hedging 101: a framework for longevity basis risk analysis and hedge effectiveness. North American Actuarial Journal15(2), 150-176. |

[5] | Cowley, A. & Cummins, J. (2005). Securitization of life insurance assets and liabilities. The Journal of Risk and Insurance72(2), 193-226. |

[6] | Dahl, M., Glar, S. & Møller, T. (2011). Mixed dynamic and static risk-minimization with an application to survivor swaps. European Actuarial Journal1(2), 233-260. |

[7] | Dahl, M., Melchior, M. & Møller, T. (2008). On systematic mortality risk and risk-minimization with survivor swaps. Scandinavian Actuarial Journal2008(2–3), 114-146. · Zbl 1224.91054 |

[8] | Fung, M. C., Ignatieva, K. & Sherris, M. (2014). Systematic mortality risk: an analysis of guaranteed lifetime withdrawal benefits in variable annuities. Insurance: Mathematics and Economics58, 103-115. · Zbl 1304.91103 |

[9] | Haberman, S., Kaishev, V., Millossovich, P. & Villegas, A. (2014). Longevity basis risk – a methodology for assessing basis risk. Report, Cass Business School and Hymans Robertson LLP. · Zbl 1390.91215 |

[10] | International Monetary Fund (IMF) (2012, April). Global financial stability report. Washington, DC: IMF. P. 123-154. |

[11] | Jarrow, R. & Turnbull, S. (1994). Delta, gamma and bucket hedging of interest rate derivatives. Applied Mathematical Finance1, 21-48. · Zbl 0831.90012 |

[12] | Li, J. & Hardy, M. R. (2011). Measuring basis risk in longevity hedges. North American Actuarial Journal15(2), 177-200. · Zbl 1228.91042 |

[13] | Luciano, E., Regis, L. & Vigna, E. (2012). Delta-gamma hedging of mortality and interest-rate risk. Insurance: Mathematics and Economics50, 402-412. · Zbl 1237.91134 |

[14] | Ngai, A. & Sherris, M. (2011). Longevity risk management for life and variable annuities: the effectiveness of static hedging using longevity bonds and derivatives. Insurance: Mathematics and Economics49, 100-114. |

[15] | Wong, T. W., Chiu, M. C. & Wong, H. Y. (2014). Time-consistent mean-variance hedging of longevity risk: effect of cointegration. Insurance: Mathematics and Economics56, 56-67. · Zbl 1304.91136 |

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